Area of trapezia
Objective. Use and explain the trapezium area formula.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
The area of a trapezium is found using the formula area = ½ × (a + b) × h, where a and b are the lengths of the two parallel sides and h is the perpendicular height between them. This formula works because a trapezium can be split into a rectangle and triangle, or doubled to form a parallelogram, confirming the averaging of the parallel sides. For parallel sides of 6 cm and 10 cm with a height of 4 cm, the area is ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32 cm². Always use the perpendicular height, not a slanted side length.
Worked example
A trapezium has parallel sides 6 cm and 10 cm and a perpendicular height of 4 cm. Find its area.
- 1Use area = ½(a + b) × h.
- 2Add the parallel sides: 6 + 10 = 16.
- 3Halve and multiply by the height: ½ × 16 × 4.
- 4Area = 32 cm².
Answer: 32 cm²
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils often use a slanting side length instead of the perpendicular height, overestimating the area of a tilted trapezium. Always measure or use the height that is perpendicular to both parallel sides.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.